Why isn't my figure consistent? It keeps changing every time

numDays = 365;

numTrials = 1000;

maxPeople = 80;

pn = zeros(maxPeople, 1);

for numPeople = 1:maxPeople

for i = (1:numTrials)

probability = 1-(1-((numPeople-1)/randi(numDays)));

end

pn(numPeople) = probability;

end

%%

figure;

ax = axes;

plot(pn)

xlabel('Value')

ylabel('Probability')

[Kevin Nelson]

I'm supposed to get an answer in which pn(22) > 0.5, but everytime I generate the code the number is too far above it, below, or exactly 0.5. Why?

[Kevin Nelson]

I mean that it should be 0.5 from 22 through 80

Answer 1

[Steven Lord]

Here's one line of your code. I've put it in block comments so MATLAB Answers won't try to execute it, since I have other code later in the answer I want to run and this line throwing an error because numPeople and numDays are not defined would prevent that.

%{
probability = 1-(1-((numPeople-1)/randi(numDays)));
%}

Since this line of code calls randi, which generates pseudorandom numbers, it's not surprising that the contents of the variable probability are different each time this line runs. If you rolled a 6-sided die over and over and always ended up with a 2, you'd be surprised (and perhaps a little angry at the person that gave you the die, for giving you a loaded die.)

n = 10;
rolls = zeros(1, n);
for whichroll = 1:n
    rolls(whichroll) = randi(6);
end
rolls

rolls = 1×10

4 2 3 2 4 5 5 1 6 6

Yes, I know I could have generated them all at once. And these rolls won't be the same as the previous ones.

otherrolls = randi(6, 1, n)

otherrolls = 1×10

2 1 5 3 1 5 4 4 3 6

[Kevin Nelson]

Then randi is not being used correctly? Then how do I implement it into my code to allow each trial to be generated a random numDays? Any other way I've tried and it always comes up with an error.

[Steven Lord]

I can't answer either of your questions because I'm not sure what problem you're trying to solve. Can you state in words (no code, no math) the problem you're trying to solve and what you intend pn and probability to represent? My first guess was that you're trying to study or simulate the birthday problem but I'm not sure.

[Kevin Nelson]

It is the birthday problem using the equation for probability. I'm supposed to be receiving a probability of >0.5 from 22 - 80, like pn(55) should be > 0.5